Semi-supervised Multi-label Learning by Solving a Sylvester Equation
Semi-supervised Multi-label Learning by Solving a Sylvester Equation
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DOI：
10.1137/1.9781611972788.37
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发表时间：
2008
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影响因子：
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通讯作者：
Gang Chen;Yangqiu Song;Fei Wang;Changshui Zhang
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文献类型：
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作者：
Gang Chen;Yangqiu Song;Fei Wang;Changshui Zhang
多标签学习是指一个实例可以被分配到多个类别的问题。本文提出了一种新的基于求解西尔维斯特方程的半监督多标签学习算法（SMSE）。首先分别在实例级和类别级构造两个图。对于实例级，基于标记和未标记实例两者来定义图，其中每个节点表示一个实例，并且每个边权重反映对应成对实例之间的相似性。类似地，对于类别级别，也基于所有类别构建图，其中每个节点表示一个类别，并且每个边权重反映对应的成对类别之间的相似性。一个正则化框架相结合的两个正则化项的两个图的建议。实例图的正则化项度量实例标签的平滑性，类别图的正则化项度量类别标签的平滑性。通过求解一个西尔维斯特方程，我们证明了未标记数据的标记最终可以得到。在RCV1数据集上的实验表明，SMSE能充分利用未标记数据信息和类别间的相关性，取得了良好的性能。此外，我们还给出了一个SMSE在协同过滤上的扩展应用。
Multi-label learning refers to the problems where an instance can be assigned to more than one category. In this paper, we present a novel Semi-supervised algorithm for Multi-label learning by solving a Sylvester Equation (SMSE). Two graphs are first constructed on instance level and category level respectively. For instance level, a graph is defined based on both labeled and unlabeled instances, where each node represents one instance and each edge weight reflects the similarity between corresponding pairwise instances. Similarly, for category level, a graph is also built based on all the categories, where each node represents one category and each edge weight reflects the similarity between corresponding pairwise categories. A regularization framework combining two regularization terms for the two graphs is suggested. The regularization term for instance graph measures the smoothness of the labels of instances, and the regularization term for category graph measures the smoothness of the labels of categories. We show that the labels of unlabeled data finally can be obtained by solving a Sylvester Equation. Experiments on RCV1 data set show that SMSE can make full use of the unlabeled data information as well as the correlations among categories and achieve good performance. In addition, we give a SMSE’s extended application on collaborative filtering.